Question

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Answer 1

Refer this attachment for your answer.

Sorry But I can't write as I don't know more about laTex and this answer needs too much latex. So refer to attachment.
Be Brainly

Answer 2

$\underline{\underline{\red{QUESTION}}}$ ➡

$\bold{If \: \bar{x} \: \: is \: \: the \: \: arithmatic \: \: mean\:of \: \: n }$
$\bold{observation ;\: \: x_1,x_2,x_3,x_4,......,x_n}$

$\bold{Show \: \: that, } \\ \\ \boxed{ \bold{(x_1 - \bar{x}) + (x_2 - \bar{ x}) + (x_3 - \bar{x}) +.... + (x_n - \bar{x})} }= 0$

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$\underline{\underline{\red{SOLUTION}}}$ ➡

$\bold{Given,} \\ \\ \bold{Arithmetic \: \: mean \: \: of \: \: n \: \: observations} \\ \bold{is \: \: \bar{x}.} \\ \\ \bold{So,} \\ \\ \bold{\frac{x_1 + x_2 + x_3 + ..... + x_n}{n} = \bar{x}} \\ \\ = > \bold{x_1 + x_2 + x_3 + .....+ x_n = n. \bar{x}} \bold{ - - - >( 1)}$

$\bold{Now,} \\ \\ \bold{L.H.S. } \\ \\ \bold{=( x_1 - \bar{x}) + (x_2 - \bar{x}) + (x_3 - \bar {x}) +.... + (x_n - \bar{x}) } \\ \\ \bold{ =( x_1 + x_2 + x_3 + ..... + x_n) - n .\bar{x}} \\ \\ \bold{ = \bar{x}.n} - \bold{n. \bar{x}} \: \: \: \: \: \: \: \: \: \bold{[from \: \: (1)]}\\ \\ \bold{ = \bar{x}n - \bar{x}n} \\ \\ = \bold{0} \\ \\ \bold{ = R.H.S.}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \underline{Hence \: \: Showed.}}$

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✝$\bold{ \red{ \mathfrak{THANKS....}}}$✝